Atmospheric data assimilation is the process of using imperfect observations of the atmosphere and imperfect computer models to estimate the past evolution of the atmosphere.

These records of past atmospheric states produced by data assimilation are used to study climate, detect model errors and initialize weather forecasts.

Many of the largest improvements in weather forecasting over the last decade have been due to improvements in data assimilation techniques. A key component of any data assimilation technique is a description of the inaccuracy of measurements of atmospheric properties such as temperature, wind velocity and humidity.

Sometimes the inaccuracy of the observation depends on the unknown true state.

This paper shows how to optimise the observational uncertainty description for data assimilation schemes in the special case of state dependent observational uncertainty.